Commutative algebra has been developed in step with algebraic geometry and has played an essential role in its foundation. In 1975, however, a new trend of commutative algebra arose with the work of Richard Stanley who used the theory of Cohen-Macaulay rings to prove affirmatively the Upper Bound Conjecture for spheres. It then turned out that commutative algebra supplies basic methods in the algebraic study of combinatorics on convex polytopes and simplicial complexes. In the last decade, combinatorial commutative algebra has been one of the most active topics in Mathematics. Almost six years ago, the study of combinatorial commutative algebra was started in Iran and now we are glad to witness that there are several colleagues and students working in this area.

It is our pleasure to inform you about the second seminar in combinatorial commutative algebra which will be held on February 8 and 9, 2012 (Bahman 19 and 20, 1390), at the School of Mathematics of IPM, Tehran, Iran.

The goal of this session is to bring together many of the people in Iran who are working in combinatorial commutative algebra, to introduce students and young researchers the topics of recent research and to set up new directions for future investigations.

• Dariush Kiani (Amirkabir University of Technology & IPM)

• Shamila Bayati (Amirkabir University of Technology)
  Squarefree Vertex Cover Algebras,
Slide Show

• Gunnar Floystad (University of Bergen, Norway)
  Extensions of Stanley-Reisner Theory: Cell Complexes and More,
Slide Show 1 Slide Show 2

• Hassan Haghighi (K. N. Toosi University of Technology)
  A Generalization of $k$-Cohen-Macaulay Simplicial Complexes


• Amir Mousivand (Islamic Azad University)
  Algebraic Properties of Product of Graphs,
Slide Show

• Abbas Nasrollah Nejad (Institute for Advanced Studies in Basic Sciences, Zanjan)
  Aluffi Torsion-free Graphs,
Slide Show

• Sara Saeedi Madani (Amirkabir University of Technology)
  On Binomial Edge Ideals


• Ali Soleyman Jahan (University of Kurdistan)
  Skeletons of $\ZZ^n$-graded Modules


• Rahim Zaare-Nahandi (University of Tehran)
  Cellular Resolutions of Transversal Monomial Ideals


• Rashid Zaare-Nahandi (Institute for Advanced Studies in Basic Sciences, Zanjan)
  Regularity of Monomial Ideals Generated in Degree 2 and 3